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Mathematical Modeling
Development of Identification Methods for Fractional Differential Equations with Riemann–Liouville Fractional Derivative
A. S. Ovsienko Samara State Technical University, Samara, 443100, Russian Federation
(published under the terms of the Creative Commons Attribution 4.0 International License)
Abstract:
The methods for parametric identification of fractional differential operators with $\alpha \in (1, 2)$ degree according to instantaneous values of experimental observations based on the Barrett differential equation example are suggested. The methods are based on construction of the linear parametrical discrete model for fractional differential equation. The coefficients of the model are associated with the required parameters of differentiation equation of fractional order. Different approaches to the determination of the relationships between the parameters of the differential equation and the discrete model coefficients are considered. Connection expressions for coefficients of linear parametrical discrete model and Cauchy type problem parameters to be identified are obtained. The algorithm of the method which let us reduce the problem to computation of mean-square estimates for coefficients of linear parametrical discrete model is described. Numerical investigations have been done; furthermore, their results let us conclude high efficiency of the methods.
Keywords:
fractional differential operators, parametric identification, linear parametrical discrete model, difference equation.
Original article submitted 19/X/2013 revision submitted – 20/XI/2013
Citation:
A. S. Ovsienko, “Development of Identification Methods for Fractional Differential Equations with Riemann–Liouville Fractional Derivative”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(34) (2014), 134–144
Linking options:
https://www.mathnet.ru/eng/vsgtu1272 https://www.mathnet.ru/eng/vsgtu/v134/p134
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Abstract page: | 453 | Full-text PDF : | 247 | References: | 65 |
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